Before discussing the meaning of this phrase, it is useful to review Isaiah's use of prophetic dualism. Prophetic dualism means that a scripture is fulfilled in more than just one event. Usually events in Isaiah's day are used as a type of things yet to come. However, sometimes the events described are both in the future. One of the best examples of this is Isaiah's statement, 'Forasmuch as this people draw near me with their mouth, and with their lips do honour me, but have removed their heart far from me' (Isaiah 29:13). When we hear this phrase, we think of the words given to Joseph Smith during the First Vision. Certainly, this phrase accurately described Joseph's day. However, the same phrase is used to describe the scribes and Pharisees in the days of the Savior (Matthew 15:8). Both interpretations are correct. The events of Isaiah's prophecy occurred twice, in the days of Jesus Christ and again in the days of Joseph Smith. Such prophetic dualism is commonly encountered when one interprets Isaiah.
The term "mountain of the Lord's house" refers to the temple. But which temple is Isaiah speaking about? Many of the brethren have interpreted this passage as having reference to the building of temples amongst the Rocky Mountains, specifically, the Salt Lake Temple. Certainly, many have come to Salt Lake from all over the world to learn of His ways and walk in His paths. Elder LeGrand Richards, while speaking of this prophecy said, "Can you go anywhere in the world and find a record of the fulfillment of that promise of Isaiah except in the gathering of the Latter-day Saints here to these valleys of the mountains?" (BYU Speeches of the Year, Feb, 10, 1960, p. 9) If this statement is true regarding the Salt Lake Temple, it must also refer to the many other temples now in use.
The gathering of people to the Salt Lake Temple does not completely fulfill the prophecy of Isaiah. Here is where prophetic dualism comes in. The scripture also has reference to the temples which will be built in Zion and in Jerusalem (2 Nephi 12:3). If Isaiah were speaking only of the temple in Salt Lake, he could have used the phrase, "the Lord's house shall be established in the valley amongst the top of the mountains." Isaiah is making reference to the mountain of the Lord's house. That means that these temples will be built on a hill or mountain to represent the spiritual journey toward God. As Hugh Nibley stated, "And the temple in Jerusalem was on the temple mountain, on Mt. Moriah. We find all the sacred places are the mountains, and they are very important here as the place of pilgrimage." (Ancient Documents and the Pearl of Great Price, Lecture 16, p. 3) Franklin D. Richards explains that the prophecy has reference to both Salt Lake and the New Jerusalem or Zion:
Franklin D. Richards
"For many years there has been a 'House of the Lord' in Salt Lake City, in the top of the mountains, and for more than thirty years, the people of many nations have been saying, 'Come...and let us go up to the mountain of the Lord.'
"That there will be a place called Zion from which 'The law shall go forth,' distinct from Jerusalem, is evident from Isaiah, 'When the Lord of Hosts shall reign in Mount Zion, and in Jerusalem;'
"How is it that Joseph Smith, Jun., first organized the means for the partial fulfilment of this prophecy, and left, at his death, the authority and instructions necessary to complete its fulfilment, by the building of a great city to be called Zion, in the state of Missouri, which in fulfilment of the prophecy, shall become the capital of this western hemisphere, if he did not obtain his knowledge of the whole matter through Divine inspiration?
"The Jaredite prophet, Ether, some 2500 years ago, foretold 'That a New Jerusalem should be built up upon this land (America), unto the seed of Joseph;' Ether 13. 4, 6." (Franklin D. Richards and James A. Little, A Compendium of the Doctrines of the Gospel, p. 106)